"""simple docstring"""


def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase							)				->   str:




						'''simple docstring'''



						_enforce_args(__lowerCAmelCase  ,       __lowerCAmelCase							)
						if n == 0:
												return 0
						lowerCamelCase__   =float("-inf"							)
						for i in range(1  ,       n + 1							):
												lowerCamelCase__   =max(
												    __lowerCAmelCase  ,       prices[i - 1] + naive_cut_rod_recursive(n - i  ,       __lowerCAmelCase							)							)

						return max_revue





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase							)				->   Any:




						'''simple docstring'''



						_enforce_args(__lowerCAmelCase  ,       __lowerCAmelCase							)
						lowerCamelCase__   =[float("-inf"							) for _ in range(n + 1							)]
						return _top_down_cut_rod_recursive(__lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)				->   Tuple:




						'''simple docstring'''



						if max_rev[n] >= 0:
												return max_rev[n]
						elif n == 0:
												return 0
						else:
												lowerCamelCase__   =float("-inf"							)
												for i in range(1  ,       n + 1							):
																		lowerCamelCase__   =max(
																		    __lowerCAmelCase  ,       prices[i - 1] + _top_down_cut_rod_recursive(n - i  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)  ,       )

												lowerCamelCase__   =max_revenue

						return max_rev[n]





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase							)				->   Dict:




						'''simple docstring'''



						_enforce_args(__lowerCAmelCase  ,       __lowerCAmelCase							)

						# length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
						# length 0.
						lowerCamelCase__   =[float("-inf"							) for _ in range(n + 1							)]
						lowerCamelCase__   =0

						for i in range(1  ,       n + 1							):
												lowerCamelCase__   =max_rev[i]
												for j in range(1  ,       i + 1							):
																		lowerCamelCase__   =max(__lowerCAmelCase  ,       prices[j - 1] + max_rev[i - j]							)

												lowerCamelCase__   =max_revenue_i

						return max_rev[n]





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase							)				->   int:




						'''simple docstring'''



						if n < 0:
												lowerCamelCase__   =F'''n must be greater than or equal to 0. Got n = {n}'''
												raise ValueError(__lowerCAmelCase							)

						if n > len(__lowerCAmelCase							):
												lowerCamelCase__   =(
												    "Each integral piece of rod must have a corresponding price. "
												    F'''Got n = {n} but length of prices = {len(__lowerCAmelCase							)}'''
												)
												raise ValueError(__lowerCAmelCase							)





def      lowerCamelCase_					(   )				->   Union[str, Any]:




						'''simple docstring'''



						lowerCamelCase__   =[6, 10, 12, 15, 20, 23]
						lowerCamelCase__   =len(__lowerCAmelCase							)

						# the best revenue comes from cutting the rod into 6 pieces, each
						# of length 1 resulting in a revenue of 6 * 6 = 36.
						lowerCamelCase__   =36

						lowerCamelCase__   =top_down_cut_rod(__lowerCAmelCase  ,       __lowerCAmelCase							)
						lowerCamelCase__   =bottom_up_cut_rod(__lowerCAmelCase  ,       __lowerCAmelCase							)
						lowerCamelCase__   =naive_cut_rod_recursive(__lowerCAmelCase  ,       __lowerCAmelCase							)

						assert expected_max_revenue == max_rev_top_down
						assert max_rev_top_down == max_rev_bottom_up
						assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
	main()



"""simple docstring"""


def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase							)				->   float:




						'''simple docstring'''



						return price * (1 + tax_rate)


if __name__ == "__main__":
	print(F'''{price_plus_tax(100, 0.25) = }''')
	print(F'''{price_plus_tax(125.50, 0.05) = }''')


